How do you use find the zeroes of f(x)=x4−4x2−45?

1 Answer
George C.
Aug 13, 2016

f(x) has zeros: 3,−3,√5i,−√5i

Explanation:

Treat as a quadratic in x2 then use the difference of squares identity:

a2−b2=(a−b)(a+b)

Note that 9⋅5=45 and 9−5=4

Hence:

x4−4x2−45

=(x2−9)(x2+5)

=(x2−32)(x2−(√5i)2)

=(x−3)(x+3)(x−√5i)(x+√5i)

Hence zeros:

3,−3,√5i,−√5i

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